Finite Group Databasebeta

← #28491690

Subgroups — #28491690

Order 15104.

500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21430066C211yesmaximal, characteristic
2#21424183C212yesmaximal
3#21422363C211yesmaximal, characteristic
4#21421976C212yesmaximal
5C59×#1280C211yesmaximal, characteristic
6C22×C4⋊Dic59C2211yescharacteristic
7#16837344—22no—
8#16837336—22no—
9#16837275—22no—
10#16837262C2212yes—
11C2×C59⋊#95—22no—
12C2×C59⋊#95C2211yescharacteristic
13#16837165—22no—
14#16837165—22no—
15C2×C22⋊C8×C59C2212yes—
16C2×#95×C59C2211yescharacteristic
17C23×Dic59—21no—
18C23×Dic59—21no—
19C2×C4⋊Dic59—22no—
20C2×C4⋊Dic59—22no—
21C2×C4⋊Dic59—21no—
22C2×C4⋊Dic59D412yes—
23C2×C4⋊Dic59D412yes—
24C2×C4⋊Dic59Q812yes—
25C2×Dic59⋊C4—22no—
26C2×Dic59⋊C4—22no—
27C2×C22⋊Dic59—22no—
28C59⋊#95—22no—
29C59⋊#95—22no—
30C59⋊#95—22no—
31C59⋊#95—22no—
32C59⋊#95—44no—
33C23×C4×C59D412yes—
34C23×C4×C59C2311yescharacteristic
35C22×C8×C59—22no—
36C22⋊C8×C59—22no—
37C22⋊C8×C59—22no—
38#95×C59—22no—
39C24×C59C2×D411yescharacteristic
40C22×C4×C59—22no—
41C22×C4×C59—22no—
42C22×C4×C59—22no—
43C22×C4×C59—42no—
44C22×C4×C59—42no—
45C22×C4×C59—42no—
46C22×C4×C59C2×D412yes—
47C22×C4×C59C2×Q811yescharacteristic
48C22×C4×C59#4112yes—
49C22×C4×C59#4111yescharacteristic
50C22×Dic59—22no—
51C22×Dic59—22no—
52C22×Dic59—22no—
53C22×Dic59—22no—
54C22×Dic59—41no—
55C22×Dic59—42no—
56C22×Dic59—41no—
57C22×Dic59—41no—
58C22×Dic59—41no—
59C22×Dic59—42no—
60C22×Dic59—42no—
61C22×Dic59—42no—
62C2×C8×C59—42no—
63C2×C8×C59—42no—
64C2×C8×C59—42no—
65C22⋊Dic59—42no—
66C22⋊Dic59—42no—
67C4⋊Dic59—24no—
68C4⋊Dic59—42no—
69C4⋊Dic59—42no—
70C4⋊Dic59—42no—
71Dic59⋊C4—82no—
72Dic59⋊C4—82no—
73C23×C59—21no—
74C23×C59—21no—
75C23×C59—22no—
76C23×C59#12011yescharacteristic
77C23×C59C22⋊Q811yescharacteristic
78C23×C59#12411yescharacteristic
79C23×C59#13512yes—
80C23×C59AGL(1,ℤ/8)12yes—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—41no—
84C2×C4×C59—42no—
85C2×C4×C59—41no—
86C2×C4×C59—44no—
87C2×C4×C59—42no—
88C2×C4×C59—42no—
89C2×C4×C59—42no—
90C2×C4×C59—82no—
91C2×C4×C59C22⋊Q812yes—
92C2×C4×C59#12412yes—
93C2×Dic59—44no—
94C2×Dic59—42no—
95C2×Dic59—42no—
96C2×Dic59—42no—
97C2×Dic59—42no—
98C2×Dic59—42no—
99C2×Dic59—42no—
100C2×Dic59—42no—
101C2×Dic59—42no—
102C2×Dic59—44no—
103C2×Dic59—82no—
104C2×Dic59—81no—
105C2×Dic59—82no—
106C2×Dic59—81no—
107C2×Dic59—81no—
108C2×Dic59—81no—
109C8×C59—82no—
110#10346—591nomaximal, Sylow
111C22×C59—22no—
112C22×C59—22no—
113C22×C59—22no—
114C22×C59—22no—
115C22×C59—21no—
116C22×C59—21no—
117C22×C59—21no—
118C22×C59—21no—
119C22×C59#39311yescharacteristic
120C22×C59#44912yes—
121C22×C59#45511yescharacteristic
122C22×C59#45611yescharacteristic
123C22×C59#45812yes—
124C22×C59#47812yes—
125C22×C59#48811yescharacteristic
126C22×C59#49011yescharacteristic
127C4×C59—22no—
128C4×C59—22no—
129C4×C59—82no—
130Dic59—82no—
131Dic59—82no—
132Dic59—82no—
133Dic59—82no—
134#2646—591no—
135#1823—592no—
136#1445—591no—
137#1294—592no—
138#1280D5911yescharacteristic
139C2×C59—21no—
140C2×C59—22no—
141C2×C59—21no—
142C2×C59#160912yes—
143C2×C59#161212yes—
144C2×C59#202511yescharacteristic
145C2×C59#202811yescharacteristic
146C2×C59#203011yescharacteristic
147C22×C4⋊C4—591no—
148C2×C22⋊C8C2×D5912yes—
149#400—1182no—
150#398—1182no—
151#385—1182no—
152#380—592no—
153C2×#95—591no—
154C2×#95—1182no—
155C2×#95C2×D5911yescharacteristic
156#340—1182no—
157#340—1182no—
158C59#1034611yescharacteristic, complemented, Sylow
159C23×C4—1181no—
160C23×C4—1181no—
161C23×C4D23612yes—
162C23×C4C22×D5911yescharacteristic
163C22×C8—22no—
164C2×C4⋊C4—592no—
165C2×C4⋊C4—592no—
166C2×C4⋊C4—592no—
167C2×C4⋊C4—1182no—
168C2×C4⋊C4—1182no—
169C2×C4⋊C4—1182no—
170C2×C4⋊C4—1182no—
171C2×C4⋊C4—1181no—
172C2×C22⋊C4—1182no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175#95—22no—
176#95—1182no—
177#95—1182no—
178#95—1182no—
179#95—1182no—
180#95—2364no—
181C24C2×D23611yescharacteristic
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—1182no—
189C22×C4—1182no—
190C22×C4—1182no—
191C22×C4—1182no—
192C22×C4—2361no—
193C22×C4—2362no—
194C22×C4—2361no—
195C22×C4—2361no—
196C22×C4—2361no—
197C22×C4—2362no—
198C22×C4—2362no—
199C22×C4—2362no—
200C22×C4#1174568512yes—
201C22×C4D4×D5912yes—
202C22×C4#1174568711yescharacteristic
203C22×C4Q8×D5911yescharacteristic
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C4⋊C4—1184no—
208C4⋊C4—4722no—
209C4⋊C4—4722no—
210C4⋊C4—2362no—
211C4⋊C4—2362no—
212C4⋊C4—2362no—
213C22⋊C4—2362no—
214C22⋊C4—2362no—
215C23—21no—
216C23—21no—
217C23—22no—
218C23#1427369711yescharacteristic
219C23#1427370711yescharacteristic
220C23#1427371511yescharacteristic
221C23#1427374912yes—
222C23#1427375512yes—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—4722no—
234C2×C4—4721no—
235C2×C4—4721no—
236C2×C4—4721no—
237C2×C4—4721no—
238C2×C4—4722no—
239C2×C4—2362no—
240C2×C4—2364no—
241C2×C4—2364no—
242C2×C4—2362no—
243C2×C4—2362no—
244C2×C4—2362no—
245C2×C4—2362no—
246C2×C4—2362no—
247C2×C4—2362no—
248C2×C4—2362no—
249C2×C4#1427370512yes—
250C2×C4#1427371312yes—
251C8—82no—
252C22—22no—
253C22—22no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—22no—
259C22—22no—
260C22#1683731511yescharacteristic
261C22#1683754912yes—
262C22#1683758211yescharacteristic
263C22#1683758711yescharacteristic
264C22#1683759312yes—
265C22#1683770312yes—
266C22#1683775711yescharacteristic
267C22#1683776711yescharacteristic
268C4—22no—
269C4—22no—
270C4—82no—
271C4—4722no—
272C4—4722no—
273C4—4722no—
274C4—4722no—
275C2—21no—
276C2—22no—
277C2—21no—
278C2#2142309512yes—
279C2#2142311212yes—
280C2#2142524311yescharacteristic
281C2#2142525811yescharacteristic
282C2#2142526411yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#1280C2
socleC23×C59#120
prime radicalC24×C59C2×D4
hypercenter#1280D59
hypocenterC59#10346
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
158. C59#10346semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214300662
#214241832
#214223632
#214219762
C59×#12802
#1034659